Question 94
Find all values of the real parameter $p$ such that the equation $|x^{2}-p x-2 p+1|=p-1$ has four real roots $x_{1}, x_{2}, x_{3}$ and $x_{4}$ such that
$$
x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}=20
$$
$$
x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}=20
$$